Preheat an oven to 350 degrees F (175 degrees C). Line a muffin pan with paper or foil liners. Sift together the flour, cocoa, and baking powder; set aside. Combine the milk, liqueur, and vanilla in a small bowl.

Beat the butter and sugar with an electric mixer in a large bowl until light and fluffy. The mixture should be noticeably lighter in color. Add the room-temperature eggs one at a time, allowing each egg to blend into the butter mixture before adding the next. Pour in the flour mixture alternately with the milk, mixing until just incorporated, ending with the flour. Pour the batter into prepared cups, about 1/2 cup each.

Press an unwrapped truffle into the bottom of each cupcake and spread the batter over the top of each truffle. Bake in a preheated oven until the tops spring back to the touch, about 20 to 25 minutes. Cool cupcakes in the pan for 5 to 10 minutes before removing to a wire rack to cool completely.